Is it possible to render animations on server, with input from other server, changing the animation?
The short answer is yes. How you do it will depend on what you have access to.

You should start by creating a script that can get the data from another machine, then move the armature with that data and send the job off to the farm. Python's urllib could be used to request data from another machine.

When you get stuck along the way, ask a more specific question. The first part of transferring data will be python specific and probably better asked on stackoverflow, once you get to blender specific tasks ask here.